You only know that Vader and Anakin are the same guy if you have seen the prequels. They talk about Anakin Skywalker as if he's a different person still.
Original Scene:
Darth Vader: What is thy bidding my master
Emperor: There is a great disturbance in the Force.
Darth Vader: I have felt it.
Darth Vader: We have a new enemy. Luke Skywalker.
Darth Vader: Yes, my master.
Emperor: He could destroy us.
Darth Vader: He's just a boy, Obi-Wan can no longer help him.
Emperor: The Force is strong with him. The son of Skywalker must not become a Jedi.
Darth Vader: If he could be turned, he would become a powerful ally.
Emperor: Yes.... Yes. He would be a great asset. Can it be done?
Darth Vader: He will join us or die Master. New Special Edition 2004 scene:
Darth Vader: What is thy bidding, my master?
Emperor: There is a great disturbance in the Force.
Darth Vader: I have felt it.
Emperor: We have a new enemy. The young rebel who destroyed the Death Star. I have no doubt, this boy is the offspring of Anakin Skywalker.
Darth Vader: How is that possible?
Emperor: Search your feelings Lord Vader, you will know it to be true. He could destroy us.
Darth Vader: He's just a boy, Obi-Wan can no longer help him.
Emperor: The Force is strong with him. The son of Skywalker must not become a Jedi.
Darth Vader: If he could be turned, he would become a powerful ally.
Emperor: Yes.... Yes. He would be a great asset. Can it be done?
Darth Vader: He will join us or die Master.
Emperor: There is a great disturbance in the Force.
Darth Vader: I have felt it.
Darth Vader: We have a new enemy. Luke Skywalker.
Darth Vader: Yes, my master.
Emperor: He could destroy us.
Darth Vader: He's just a boy, Obi-Wan can no longer help him.
Emperor: The Force is strong with him. The son of Skywalker must not become a Jedi.
Darth Vader: If he could be turned, he would become a powerful ally.
Emperor: Yes.... Yes. He would be a great asset. Can it be done?
Darth Vader: He will join us or die Master. New Special Edition 2004 scene:
Darth Vader: What is thy bidding, my master?
Emperor: There is a great disturbance in the Force.
Darth Vader: I have felt it.
Emperor: We have a new enemy. The young rebel who destroyed the Death Star. I have no doubt, this boy is the offspring of Anakin Skywalker.
Darth Vader: How is that possible?
Emperor: Search your feelings Lord Vader, you will know it to be true. He could destroy us.
Darth Vader: He's just a boy, Obi-Wan can no longer help him.
Emperor: The Force is strong with him. The son of Skywalker must not become a Jedi.
Darth Vader: If he could be turned, he would become a powerful ally.
Emperor: Yes.... Yes. He would be a great asset. Can it be done?
Darth Vader: He will join us or die Master.